{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 第6章 数据的统计分析及可视化"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.1 随机变量及其分布"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 　6.1.1 均匀分布及随机数图"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6.1.1.1 均匀分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np                        #加载numpy包\n",
    "np.set_printoptions(precision=4)          #设置numpy输出为4位有效数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.    , 0.0526, 0.1053, 0.1579, 0.2105, 0.2632, 0.3158, 0.3684,\n",
       "       0.4211, 0.4737, 0.5263, 0.5789, 0.6316, 0.6842, 0.7368, 0.7895,\n",
       "       0.8421, 0.8947, 0.9474, 1.    ])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a=0;b=1;n=20            # n表示在[a,b]中生成n个点\n",
    "x=np.linspace(a,b,n);   # [a,b]中n个等差数据\n",
    "ｘ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1.])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y=np.ones(n)/(b-a);y    # y=1/(b-a)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt               \n",
    "plt.plot(x,y);plt.ylim(0,1.5);plt.stem(x,y);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6.1.1.2 均匀随机数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（1）生成一个均匀随机实数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.3765])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.rand(1)   #生成[0,1]上的一个随机实数:random.uniform(0,1)     "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（2）生成一组随机实数及图示"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.6965, 0.2861, 0.2269, 0.5513, 0.7195, 0.4231, 0.9808, 0.6848,\n",
       "       0.4809, 0.3921])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(123)            #设置种子数seed可重复结果,可任意设置\n",
    "R=np.random.rand(10);R[:10]  #[0,1]上的1000个随机数=np.random.uniform(0,1,1000) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(R,'.');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 　6.1.2 正态分布及随机数图"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6.1.2.1  正态分布函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（1）标准正态分布曲线"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import arange,exp  #arange类似linspace函数\n",
    "from math import sqrt,pi   \n",
    "x=arange(-4,4,0.1)            #x为-4到4上间距为0.1的数   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y=1/sqrt(2*pi)*exp(-x**2/2);\n",
    "plt.plot(x,y);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（2）标准正态分布的取值(pdf)及分位数(ppf)计算"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.05399096651318806"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import scipy.stats as st  #加载统计方法包 \n",
    "p_z=st.norm.pdf(-2);p_z   #p(z)=1/sqrt(2*pi)*exp(-z**2/2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.6448536269514722"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "za=st.norm.ppf(0.95);za   #单侧"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-1.9599639845400545, 1.959963984540054]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[st.norm.ppf(0.025),st.norm.ppf(0.975)] #双侧"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（3）标准正态分布的概率计算"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9500150944608786"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p=st.norm.cdf(1.645);p       #标准正态分布下的面积：p=P(z≤1.645)的累积概率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    " #标准正态曲线下[a,b]上计算概率的面积图\n",
    "import scipy.stats as st  #加载统计方法包 \n",
    "def norm_p(a,b):            \n",
    "        x=np.arange(-4,4,0.1) \n",
    "        y=st.norm.pdf(x)         \n",
    "        x1=x[(a<=x) & (x<=b)];x1 \n",
    "        y1=y[(a<=x) & (x<=b)];y1         \n",
    "        p=st.norm.cdf(b)-st.norm.cdf(a);\n",
    "        print(\"    N(0,1)分布: [%3.2f,%3.2f]  p=%5.4f\"%(a,b,p)) \n",
    "        plt.plot(x,y);#plt.text(-0.7,0.2,\"p=%5.4f\"%p,fontsize=15);\n",
    "        plt.hlines(0,-4,4); plt.vlines(x1,0,y1,colors='r');         "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    N(0,1)分布: [-4.00,-2.00]  p=0.0227\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "norm_p(-4,-2)       # p=P(z≤2)=0.27%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    N(0,1)分布: [-2.00,2.00]  p=0.9545\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "norm_p(-2,2)        # p=P(-2≤z≤2)=95.45%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    N(0,1)分布: [-1.96,1.96]  p=0.9500\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "norm_p(-1.96,1.96)  # p=P(-1.96≤z≤1.96)=95% "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6.1.2.2 正态分布随机数图"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（1）标准正态随机数及分布图 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.2659, -0.8667, -0.6789, -0.0947,  1.4914])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.normal(0,1,5)    #生成 5 个标准正态分布随机数 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.6389, -0.444 , -0.4344,  2.2059,  2.1868,  1.0041,  0.3862,\n",
       "        0.7374,  1.4907, -0.9358,  1.1758, -1.2539, -0.6378,  0.9071,\n",
       "       -1.4287, -0.1401, -0.8618, -0.2556, -2.7986, -1.7715])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#随机产生1000个标准正态分布随机数，作其概率直方图，然后再添加正态分布的密度函数线。\n",
    "#np.random.seed(123)             #设置种子数seed可使结果可重复\n",
    "z1=np.random.normal(0,1,1000)   #1000个标准正态分布随机数N(0,1)\n",
    "z1[:20]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(z1);                   #可设定分段数bins, plt.hist(z1,bins=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(456)            #设置种子seed可重复结果\n",
    "z2=np.random.normal(0,1,1000)\n",
    "plt.hist(z2);#plt.ylim=[0,400];"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(z1); plt.hist(z2);    #做在一张图上"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9X+5eVaer6qlu+xXgOQYrOTVFPe3Po/S+r4/Sx++B4T6/jwD/Mu0imH+5e2+DM8kc8FbgR1MuRZfqS38eZab6+ih9+R70/mEdqynJ94A/muetz1bVI90+nwXOAw+uZW2zLskbgG8B91TVb6Zdz3pgf+6fPn0P1lW4V9W7R72f5K+BvwRurX5cjJiJ5e5JXs+gQz9YVd+edj3rxQz251Fmoq+P0rfvgRdUO0luA74M/HlVnZt2PQBJXsfgItOtDDr6E8Bf9WlVZJIAB4BfVdU9Uy5HnT7251Fmoa+P0sfvgeHeSXIcuBL4Zdf0eFX97RRLAiDJ7cA/8Lvl7nunW9GlkrwT+E/gJ8CrXfNnqurQ9KpSX/vzKH3v66P08XtguEtSg5wtI0kNMtwlqUGGuyQ1yHCXpAYZ7pLUIMNdkhpkuEtSg/4fLH5lcE/d6ggAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#一页绘制2个正态分布随机图\n",
    "plt.subplot(121);plt.hist(z1); \n",
    "plt.subplot(122);plt.hist(z2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>z1</th>\n",
       "      <th>z2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.638902</td>\n",
       "      <td>-0.668129</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.443982</td>\n",
       "      <td>-0.498210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.434351</td>\n",
       "      <td>0.618576</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.205930</td>\n",
       "      <td>0.568692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.186786</td>\n",
       "      <td>1.350509</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>995</th>\n",
       "      <td>-0.807699</td>\n",
       "      <td>2.591205</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>996</th>\n",
       "      <td>-1.276077</td>\n",
       "      <td>-0.468390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>997</th>\n",
       "      <td>0.553626</td>\n",
       "      <td>0.898201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998</th>\n",
       "      <td>0.553874</td>\n",
       "      <td>-0.669727</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999</th>\n",
       "      <td>-0.691200</td>\n",
       "      <td>0.019731</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1000 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           z1        z2\n",
       "0   -0.638902 -0.668129\n",
       "1   -0.443982 -0.498210\n",
       "2   -0.434351  0.618576\n",
       "3    2.205930  0.568692\n",
       "4    2.186786  1.350509\n",
       "..        ...       ...\n",
       "995 -0.807699  2.591205\n",
       "996 -1.276077 -0.468390\n",
       "997  0.553626  0.898201\n",
       "998  0.553874 -0.669727\n",
       "999 -0.691200  0.019731\n",
       "\n",
       "[1000 rows x 2 columns]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "z12=pd.DataFrame({'z1':z1,'z2':z2}); z12 #构建数据框"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "z12.plot(kind='hist'); #根据数据框绘直方图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "z12.plot(kind='hist',subplots=True,layout=(1,2));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "z12.plot(kind='density',subplots=True,layout=(1,2)); #模拟正态分布曲线"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（2）一般正态随机数及分布图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([174.7, 163.2, 172.4, 153. , 177.5, 154.7, 170.1, 168.8, 161.9,\n",
       "       198.7, 164. , 174.7, 181. , 157.8, 183.4, 168.8, 180.1, 160.9,\n",
       "       159.7, 182.1, 175. , 171.4, 176.4, 175.3, 158.5, 147.9, 153.2,\n",
       "       152.1, 147.8, 163.5, 164.7, 169.6, 172.1, 166.2, 167.5, 170.7,\n",
       "       160. , 162.9, 170.4, 163.2, 164.3, 168.9, 183.4, 173.2, 166.6,\n",
       "       164.1, 168.9, 192.4, 138.5, 175.4, 172.3, 178.7, 158.5, 191.1,\n",
       "       180. , 169.5, 171.6, 162.8, 170.5, 168.6, 179.4, 173.6, 169.2,\n",
       "       176.8, 175.6, 172.2, 154.7, 180.3, 158.3, 159.9, 168.9, 175.1,\n",
       "       184.1, 153.1, 184.7, 186.4, 165.4, 168. , 164.3, 164. , 156.6,\n",
       "       153.1, 168. , 172.6, 188.3, 160. , 149.1, 171.5, 165.3, 173.6,\n",
       "       166. , 157.4, 163.1, 178. , 172.7, 160.3, 178.7, 155.5, 164.6,\n",
       "       172. ])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(12)   #设置种子数seed可重复结果\n",
    "X=np.random.normal(170,10,100); X.round(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import warnings  \n",
    "warnings.filterwarnings(\"ignore\")            #忽略警告信息\n",
    "import seaborn as sns\n",
    "sns.distplot(X);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（3）非正态随机数及分布图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.7317, 1.4039, 0.8556, 0.6054, 1.2656, 0.1714, 0.3343, 0.337 ,\n",
       "       0.737 , 0.6227])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(15)  #设置种子数seed可重复结果\n",
    "Y=np.random.lognormal(0,1,1000); Y[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(Y);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Z=np.log(Y)      # Z=log(Y)\n",
    "sns.distplot(Z);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6.1.2.3 正态分布概率检验图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import scipy.stats as st   #加载科学计算包scipy的统计功能\n",
    "st.probplot(X,plot=plt);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "st.probplot(Y,plot=plt); "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "st.probplot(Z, plot=plt); "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.2 统计量及抽样分布图"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 　6.2.1 统计量及抽样的概念"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6.2.1.1 简单随机模拟"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（1）生成[0,1]上的一组随机整数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0,\n",
       "       0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1,\n",
       "       0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1,\n",
       "       0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.randint(0,2,100)    #[0,1]上的10个随机整数 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（2）生成任意区间上的一组随机整数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([32, 86, 52, 60, 20, 14,  3, 28, 31, 75])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.randint(1,101,10)  #[1,100]上的10个随机整数数组"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([73, 13,  6,  1, 29, 28, 72, 76, 86, 48])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(15)           #结果可重复\n",
    "np.random.randint(1,101,10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6.2.1.2 随机抽样方法"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（1）根据随机数抽样"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>学号</th>\n",
       "      <th>性别</th>\n",
       "      <th>身高</th>\n",
       "      <th>体重</th>\n",
       "      <th>支出</th>\n",
       "      <th>开设</th>\n",
       "      <th>课程</th>\n",
       "      <th>软件</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1510248008</td>\n",
       "      <td>女</td>\n",
       "      <td>167</td>\n",
       "      <td>71</td>\n",
       "      <td>46.0</td>\n",
       "      <td>不清楚</td>\n",
       "      <td>都未学过</td>\n",
       "      <td>No</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1510229019</td>\n",
       "      <td>男</td>\n",
       "      <td>171</td>\n",
       "      <td>68</td>\n",
       "      <td>10.4</td>\n",
       "      <td>有必要</td>\n",
       "      <td>概率统计</td>\n",
       "      <td>Matlab</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1512108019</td>\n",
       "      <td>女</td>\n",
       "      <td>175</td>\n",
       "      <td>73</td>\n",
       "      <td>21.0</td>\n",
       "      <td>有必要</td>\n",
       "      <td>统计方法</td>\n",
       "      <td>SPSS</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1512332010</td>\n",
       "      <td>男</td>\n",
       "      <td>169</td>\n",
       "      <td>74</td>\n",
       "      <td>4.9</td>\n",
       "      <td>有必要</td>\n",
       "      <td>编程技术</td>\n",
       "      <td>Excel</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1512331015</td>\n",
       "      <td>男</td>\n",
       "      <td>154</td>\n",
       "      <td>55</td>\n",
       "      <td>25.9</td>\n",
       "      <td>有必要</td>\n",
       "      <td>都学习过</td>\n",
       "      <td>Python</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>1538319004</td>\n",
       "      <td>男</td>\n",
       "      <td>175</td>\n",
       "      <td>68</td>\n",
       "      <td>44.4</td>\n",
       "      <td>不清楚</td>\n",
       "      <td>统计方法</td>\n",
       "      <td>SAS</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>1538254010</td>\n",
       "      <td>女</td>\n",
       "      <td>166</td>\n",
       "      <td>65</td>\n",
       "      <td>5.3</td>\n",
       "      <td>不清楚</td>\n",
       "      <td>编程技术</td>\n",
       "      <td>Python</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>1540294017</td>\n",
       "      <td>女</td>\n",
       "      <td>159</td>\n",
       "      <td>58</td>\n",
       "      <td>71.4</td>\n",
       "      <td>不清楚</td>\n",
       "      <td>都学习过</td>\n",
       "      <td>SPSS</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>1540365026</td>\n",
       "      <td>女</td>\n",
       "      <td>169</td>\n",
       "      <td>73</td>\n",
       "      <td>5.5</td>\n",
       "      <td>有必要</td>\n",
       "      <td>统计方法</td>\n",
       "      <td>Excel</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>1540388036</td>\n",
       "      <td>女</td>\n",
       "      <td>165</td>\n",
       "      <td>67</td>\n",
       "      <td>56.8</td>\n",
       "      <td>不必要</td>\n",
       "      <td>概率统计</td>\n",
       "      <td>SAS</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>52 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            学号 性别   身高  体重    支出   开设    课程      软件\n",
       "0   1510248008  女  167  71  46.0  不清楚  都未学过      No\n",
       "1   1510229019  男  171  68  10.4  有必要  概率统计  Matlab\n",
       "2   1512108019  女  175  73  21.0  有必要  统计方法    SPSS\n",
       "3   1512332010  男  169  74   4.9  有必要  编程技术   Excel\n",
       "4   1512331015  男  154  55  25.9  有必要  都学习过  Python\n",
       "..         ... ..  ...  ..   ...  ...   ...     ...\n",
       "47  1538319004  男  175  68  44.4  不清楚  统计方法     SAS\n",
       "48  1538254010  女  166  65   5.3  不清楚  编程技术  Python\n",
       "49  1540294017  女  159  58  71.4  不清楚  都学习过    SPSS\n",
       "50  1540365026  女  169  73   5.5  有必要  统计方法   Excel\n",
       "51  1540388036  女  165  67  56.8  不必要  概率统计     SAS\n",
       "\n",
       "[52 rows x 8 columns]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "pd.set_option('display.max_rows', 10)\n",
    "BSdata=pd.read_excel('DaPy_data.xlsx','BSdata');   #读取学生数据\n",
    "BSdata"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([30, 18, 46, 32, 24, 33])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i=np.random.randint(1,53,6);i #抽取6名学生，取[1,52]上的6个整数 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>学号</th>\n",
       "      <th>性别</th>\n",
       "      <th>身高</th>\n",
       "      <th>体重</th>\n",
       "      <th>支出</th>\n",
       "      <th>开设</th>\n",
       "      <th>课程</th>\n",
       "      <th>软件</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>1529365032</td>\n",
       "      <td>男</td>\n",
       "      <td>172</td>\n",
       "      <td>71</td>\n",
       "      <td>10.4</td>\n",
       "      <td>有必要</td>\n",
       "      <td>都学习过</td>\n",
       "      <td>SPSS</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1524105026</td>\n",
       "      <td>女</td>\n",
       "      <td>163</td>\n",
       "      <td>65</td>\n",
       "      <td>69.4</td>\n",
       "      <td>有必要</td>\n",
       "      <td>编程技术</td>\n",
       "      <td>Python</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>1438120022</td>\n",
       "      <td>男</td>\n",
       "      <td>166</td>\n",
       "      <td>70</td>\n",
       "      <td>35.6</td>\n",
       "      <td>有必要</td>\n",
       "      <td>统计方法</td>\n",
       "      <td>R</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>1530243029</td>\n",
       "      <td>男</td>\n",
       "      <td>186</td>\n",
       "      <td>87</td>\n",
       "      <td>9.5</td>\n",
       "      <td>不必要</td>\n",
       "      <td>都未学过</td>\n",
       "      <td>No</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1527173011</td>\n",
       "      <td>女</td>\n",
       "      <td>160</td>\n",
       "      <td>62</td>\n",
       "      <td>11.5</td>\n",
       "      <td>不必要</td>\n",
       "      <td>都学习过</td>\n",
       "      <td>Matlab</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>1531364037</td>\n",
       "      <td>女</td>\n",
       "      <td>171</td>\n",
       "      <td>69</td>\n",
       "      <td>7.3</td>\n",
       "      <td>有必要</td>\n",
       "      <td>都学习过</td>\n",
       "      <td>Excel</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            学号 性别   身高  体重    支出   开设    课程      软件\n",
       "30  1529365032  男  172  71  10.4  有必要  都学习过    SPSS\n",
       "18  1524105026  女  163  65  69.4  有必要  编程技术  Python\n",
       "46  1438120022  男  166  70  35.6  有必要  统计方法       R\n",
       "32  1530243029  男  186  87   9.5  不必要  都未学过      No\n",
       "24  1527173011  女  160  62  11.5  不必要  都学习过  Matlab\n",
       "33  1531364037  女  171  69   7.3  有必要  都学习过   Excel"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "BSdata.iloc[i]                 #获取抽到的6名学生信息 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（2）直接抽取样本（sample）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>学号</th>\n",
       "      <th>性别</th>\n",
       "      <th>身高</th>\n",
       "      <th>体重</th>\n",
       "      <th>支出</th>\n",
       "      <th>开设</th>\n",
       "      <th>课程</th>\n",
       "      <th>软件</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1524105026</td>\n",
       "      <td>女</td>\n",
       "      <td>163</td>\n",
       "      <td>65</td>\n",
       "      <td>69.4</td>\n",
       "      <td>有必要</td>\n",
       "      <td>编程技术</td>\n",
       "      <td>Python</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>1531364037</td>\n",
       "      <td>女</td>\n",
       "      <td>171</td>\n",
       "      <td>69</td>\n",
       "      <td>7.3</td>\n",
       "      <td>有必要</td>\n",
       "      <td>都学习过</td>\n",
       "      <td>Excel</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>1538399025</td>\n",
       "      <td>男</td>\n",
       "      <td>169</td>\n",
       "      <td>65</td>\n",
       "      <td>9.5</td>\n",
       "      <td>有必要</td>\n",
       "      <td>统计方法</td>\n",
       "      <td>SAS</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>1529314037</td>\n",
       "      <td>男</td>\n",
       "      <td>170</td>\n",
       "      <td>70</td>\n",
       "      <td>15.1</td>\n",
       "      <td>有必要</td>\n",
       "      <td>概率统计</td>\n",
       "      <td>SAS</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>1529365032</td>\n",
       "      <td>男</td>\n",
       "      <td>172</td>\n",
       "      <td>71</td>\n",
       "      <td>10.4</td>\n",
       "      <td>有必要</td>\n",
       "      <td>都学习过</td>\n",
       "      <td>SPSS</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>1537288004</td>\n",
       "      <td>女</td>\n",
       "      <td>173</td>\n",
       "      <td>70</td>\n",
       "      <td>19.1</td>\n",
       "      <td>不清楚</td>\n",
       "      <td>编程技术</td>\n",
       "      <td>Python</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            学号 性别   身高  体重    支出   开设    课程      软件\n",
       "18  1524105026  女  163  65  69.4  有必要  编程技术  Python\n",
       "33  1531364037  女  171  69   7.3  有必要  都学习过   Excel\n",
       "45  1538399025  男  169  65   9.5  有必要  统计方法     SAS\n",
       "28  1529314037  男  170  70  15.1  有必要  概率统计     SAS\n",
       "30  1529365032  男  172  71  10.4  有必要  都学习过    SPSS\n",
       "42  1537288004  女  173  70  19.1  不清楚  编程技术  Python"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "BSdata.sample(6)             #直接抽取名学生及其信息 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 　6.2.2 统计量的分布"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6.2.2.1 中心极限定理及其模拟图"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（1）正态均值的分布—正态分布 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 基于正态分布的中心极限定理模拟函数\n",
    "import seaborn as sns\n",
    "def norm_sim1(N=1000,n=10):    # n为样本个数，N为模拟次数（即抽样次数） \n",
    "    xbar=np.zeros(N)           # 产生放置样本均值的向量  \n",
    "    for i in range(N):         # 计算[0,1]上的标准正态随机数及均值 \n",
    "        xbar[i]=np.random.normal(0,1,n).mean() \n",
    "    sns.distplot(xbar,bins=50) #plt.hist(xbar,bins=50)   \n",
    "    print(pd.DataFrame(xbar).describe().T) #模拟结果的基本统计量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     count      mean       std       min       25%       50%       75%  \\\n",
      "0  10000.0  0.002303  0.184125 -0.751992 -0.121302  0.002808  0.128373   \n",
      "\n",
      "        max  \n",
      "0  0.770898  \n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(1)         #设置种子数seed使结果可重复\n",
    "norm_sim1(10000,30)               #根据默认值模拟"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     count      mean       std       min       25%       50%       75%  \\\n",
      "0  10000.0 -0.003134  0.181091 -0.612653 -0.127927 -0.002509  0.120398   \n",
      "\n",
      "        max  \n",
      "0  0.684151  \n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(2)        #设置种子数seed使结果可重复\n",
    "norm_sim1(n=30,N=10000)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（２）非正态均值统计量的分布 —— 渐近正态分布"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 基于非正态分布的中心极限定理模拟函数\n",
    "def norm_sim2(N=1000,n=10): \n",
    "    xbar=np.zeros(N) \n",
    "    for i in range(N):  #计算[0,1]上的均匀随机数及均值 \n",
    "        xbar[i]=np.random.uniform(0,1,n).mean()  \n",
    "    sns.distplot(xbar,bins=50)\n",
    "    print(pd.DataFrame(xbar).describe().T) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    count      mean       std       min       25%       50%       75%  \\\n",
      "0  1000.0  0.496785  0.090672  0.203241  0.436412  0.497801  0.560534   \n",
      "\n",
      "        max  \n",
      "0  0.732275  \n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(3)   #设置种子数seed使结果可重复\n",
    "norm_sim2() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     count      mean       std       min       25%       50%       75%  \\\n",
      "0  10000.0  0.499467  0.052163  0.294711  0.463689  0.499249  0.534502   \n",
      "\n",
      "        max  \n",
      "0  0.711937  \n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(4)   #设置种子数seed使结果可重复\n",
    "norm_sim2(10000,30) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6.2.2.2 均值的 t 分布及其图示"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（１）小样本正态均值的标准化统计量分布 — t分布"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（2）t 分布曲线比较图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=np.arange(-4,4,0.1) \n",
    "yn=st.norm.pdf(x,0,1); yt3=st.t.pdf(x,3); yt10=st.t.pdf(x,30) \n",
    "plt.plot(x,yn,'r-',x,yt3,'b.',x,yt10,'g-.'); \n",
    "plt.legend([\"N(0,1)\",\"t(3)\",\"t(10)\"]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.3 基本统计推断方法"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 　6.3.1 参数的估计方法"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6.3.1.1 点估计 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "BSdata=pd.read_excel('DaPy_data.xlsx','BSdata');   #读取学生数据\n",
    "#BSdata"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（1）均值的点估计"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "168.51923076923077"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "BSdata['身高'].mean() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（2）标准差的点估计"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.01833776871194"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "BSdata['身高'].std() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（3）比例的点估计 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "有必要    0.557692\n",
       "不清楚    0.230769\n",
       "不必要    0.211538\n",
       "Name: 开设, dtype: float64"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f=BSdata['开设'].value_counts(); \n",
    "p=f/sum(f);p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.28"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#假定有 150 人接受调查，其中 42 人喜欢品牌 A，问喜欢 A 品牌的人占多大比例？\n",
    "42/150"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6.3.1.2 区间估计"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    N(0,1)分布: [-2.00,2.00]  p=0.9545\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "norm_p(-2,2) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.stats as st\n",
    "def t_p(a,b,df=10):  #t分布曲线下[a,b]上计算概率的面积图\n",
    "        x=np.arange(-4,4,0.1) \n",
    "        y=st.t.pdf(x,df)         \n",
    "        x1=x[(a<=x) & (x<=b)];x1 \n",
    "        y1=y[(a<=x) & (x<=b)];y1 \n",
    "        p=st.t.cdf(b,df)-st.t.cdf(a,df);\n",
    "        print(\"      t(\"+str(df)+\"): [%3.2f, %3.2f]  p=%5.4f\"%(a,b,p)) \n",
    "        plt.plot(x,y);#plt.text(-0.7,0.2,\"p=%5.4f\"%p,fontsize=15);\n",
    "        plt.hlines(0,-4,4); plt.vlines(x1,0,y1,colors='r'); "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      t(10): [-2.00, 2.00]  p=0.9266\n"
     ]
    },
    {
     "data": {
      "image/png": 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Ur3XfmB7p9sqWiLiBWcAVQCVQJCLzVbWkw2GrgUJVPSwi9wKPA7f49x1R1YnBjW2ixQef1/LcX/6N03JT4GsfOx3HcS6XMPvFh6itb+LwLatI8ETvxWkTuEBa9JOBMlUtV9VmYDYwveMBqvquqh6dMHs5kB/cmCZavblxF26XkBIX63SUkJGR6MGnyvultU5HMWEikEKfB1R0eF7p33Y8dwOLOzyPE5FiEVkuItd3dYKI3OM/pri21n54TbvmVh/vlNSQnujBem3+n5S4WGLcLhbbJGcmQEH9u09EbgMKgYs7bB6qqlUiMgJYKiLrVXVLx/NU9WngaYDCwkINZiYTvpaV76WusTVqb5I6HhHISPCw9LPdNLW24Y2J3HVzTXAE0qKvAgZ3eJ7v3/YFInI58GNgmqo2Hd2uqlX+/5YD7wGTepHXRJE3N1ST6HGTFm/dNp2lJ3o41NTKR5v3OB3FhIFACn0RUCAiw0XEA8wAvjB6RkQmAU/RXuR3d9ieLiJe/+NM4Hyg40VcY7rU5lPe2ljDpadl4xLrt+ksNT6W5LgYm6PeBKTbrhtVbRWRmcASwA08p6obReQxoFhV5wNPAEnAK9L+odyhqtOA04GnRMRH+y+VX3carWNMl4q27WNvQzNTxkb3TVLH4xK4/PSBvL2phpY2H7FuuyXGHF9AffSqughY1Gnbox0eX36c8z4BxvUmoIlOb27YhTfGxaWnZjsdJWRNGZvDvNVVfFq+jwsKMp2OY0KYNQNMyPH5lDc37OKiUVkkRvEkZt25qCCL+Fi33TxlumWF3oSctZUH2FXXyFTrtjmheI+bS0/LYsnGGtp8NljNHJ8VehNy3tywi1i3cNnpA52OEvKmjM1lz6EmVu3Y73QUE8Ks0JuQoqos3rCL807JJNWGVXbrK6dl43G7WLzeRt+Y47MOUBNSNu6s4/Env8+IrCS4a5nTcUJekjeGN+Y+QsNLrfiuWYPLbiE2XbAWvQkpizdUgwjpCXY3bKAykjw0t/pYW3nA6SgmRFmhNyFDVVm0fhepcTHEuq1lGqj0BA8iYnPfmOOyQm9CRmlNPVv3NNjcNj0U4xJS42NZtL4aVRt9Y77MCr0JGYvW78Il7fO4mJ7JSPRQuf8IG6rqnI5iQpAVehMyFq2vZvLwDDx2O3+PZSR6iHEJC9fbzVPmy+wTZULC5pp6ynYf4ppxuU5HCUsxLuG8kZks3mDdN+bLrNCbkLBo/S5E4Koxdjfsybp6bA7b9x6mpNq6b8wXWaE3IWHxhmrOGppBdkqc01HC1pVjcnC7xG6eMl9ihd44bkvtIT7bVc/Ucdaa742MRA/njMiw0TfmS6zQG8ct9l9AtLnne2/q2FzK9zRQWlPvdBQTQmwKBOO4i+65mUtckPvr1U5HCXtXjclh5M3Xkrg4HtaucDqOCREBtehFZIqIlIpImYg82MX++0WkRETWicg/RWRoh313ishm/9edwQxvwl/Z7kMcbm5lQKLX6SgRISvZS0p8LHsPNVv3jTmm20IvIm5gFjAVGA3cKiKjOx22GihU1fHAq8Dj/nMzgJ8CZwOTgZ+KSHrw4ptwt2DdTgAGJNlNUsEyIMlLY0sbG3fa6BvTLpAW/WSgTFXLVbUZmA1M73iAqr6rqof9T5cD+f7HVwFvq+o+Vd0PvA1MCU50E+5UlTfW7iQ5LtZukgqiDP/cNwvW2c1Tpl0gn648oKLD80r/tuO5G1jck3NF5B4RKRaR4tra2gAimUjw2a56ttQ2WGs+yGLdQkp8LAvW7bTuGwMEedSNiNwGFAJP9OQ8VX1aVQtVtTArKyuYkUwIW7BuJ26XMMDmtgm6TP/cN2sqDjgdxYSAQAp9FTC4w/N8/7YvEJHLgR8D01S1qSfnmuijqixYV815pwwg1rptgi490YPH7bLuGwMEVuiLgAIRGS4iHmAGML/jASIyCXiK9iK/u8OuJcCVIpLuvwh7pX+biXLrqw6yfe9hrhs/yOkoESnGJVx8ahYL11Xjs4XDo163hV5VW4GZtBfoTcAcVd0oIo+JyDT/YU8AScArIrJGROb7z90H/Iz2XxZFwGP+bSbKLVhXTaxbbG6bPnTt+Fx21TVSvN0WDo92Ad0wpaqLgEWdtj3a4fHlJzj3OeC5kw1oIo/PpyxcV82FBVmkJtgC4H3l8tMHEhfrYsG6nUwenuF0HOMg6xw1/W51xX6qDhzhugk2JXFfSvTGcNlpA1m0vprWNp/TcYyDrNCbfvfG2mo8MS4uP32g01Ei3rXjc9lzqJll5XudjmIcZIXe9KuWNh/X3vd1Fsz9Cclx1m3T1y49LZtXZj9E7vVTnY5iHGSF3vSrjzbvobXNR2ayjZ3vD3GxbjISvexraOZIc5vTcYxDrNCbfjVvdRUxbhdp8Vbo+0tmkgefT3l7U43TUYxDrNCbfnOoqZW3SnYxINGDS5xOEz1S4mPxxLj4x2q7VzFaWaE3/WbJhl00tvjITLIpifuTAJlJXt7/vJa9h5q6Pd5EHiv0pt/MW13FkIwEkuJsvZv+lpnkpc3XPluoiT5W6E2/qKlr5OMte7h+Uh7Wa9P/EjxuRuemMG+NFfpoZIXe9Iv5a3aiCtdPtLltnPLVSXmsrThAee0hp6OYfmaF3vSLeaurmDA4jRFZSU5HiVrTJg5CBP5hrfqoY4Xe9LnPa+opqa7jq9aad9TAlDjOPyWTf6yusgVJooxdFTN9znvFZbx8sJFTHilyOkrU+8//+QFbag9RdNP7NtFZFLEWvelTLW0+9tQ3kZYQa8MqQ0BGkge3S3i5qKL7g03EsEJv+tTSz3bT0uYjO9mKfChwizAgycui9dXUN7Y4Hcf0Eyv0pk/NKaog1qY8CClZyV6OtLTZMoNRxAq96TM1dY28W7qbrGQvYoPnQ0aSN4aC7CTmFFv3TbQIqNCLyBQRKRWRMhF5sIv9F4nIKhFpFZEbO+1r8y8veGyJQRMd5q6qxKftLUgTOgS45azBrN5xgM019U7HMf2g20IvIm5gFjAVGA3cKiKjOx22A/gm8GIXL3FEVSf6v6Z1sd9EIFXlleJKJg/PID7W7XQc08lXJ+UR4xJr1UeJQFr0k4EyVS1X1WZgNjC94wGquk1V1wG2XpkBoGjbfrbuaeDmwsFORzFdGJDk5fLTB/LaqiqaW+1jG+kCKfR5QMdf+5X+bYGKE5FiEVkuItd3dYCI3OM/pri2trYHL21C1ZziCpK8MVw9LsfpKOY4bjlrMHsbmln62W6no5g+1h8XY4eqaiHwdeB3InJK5wNU9WlVLVTVwqysrH6IZPpSfWMLC9dVc92EXBI8dk9eqLqwIJOBKV7rvokCgXwKq4COf3/n+7cFRFWr/P8tF5H3gEnAlh5kNGFm3uoq/vz8vzH2nVT42kdOxzHHEeN28erLD1O1/wgV0z5lcEaC05FMHwmkRV8EFIjIcBHxADOAgEbPiEi6iHj9jzOB84GSkw1rQp+q8rdl20n0xpDktdZ8qMtOjgPgxRU7HE5i+lK3hV5VW4GZwBJgEzBHVTeKyGMiMg1ARM4SkUrgJuApEdnoP/10oFhE1gLvAr9WVSv0EWx5+T427z7EwJQ4p6OYAHhjXKQneni5qILGFls8PFIF1ORS1UXAok7bHu3wuIj2Lp3O530CjOtlRhNG/rZ8m39eG7sTNlzkpMSxr6GZReur+doZX/oYmwhgd8aaoNl1sJElG2u4uXAwLrsVNmykxMcyIiuRvy7b7nQU00es0JugeXHFDnyq3Hb2UKejmB4Q4PZzhrKm4gDrKw86Hcf0ASv0JiiaW328tGIHl4zKYsgAG70Rbm44M5/4WDd/XbbN6SimD1ihN0HxVskuauubuP1ca82Ho5S4WK6flMf8tTs5cLjZ6TgmyKzQm6D467LtDM6I5+JR2U5HMSfpjnOH0tTqsxuoIpANdDa9tr7yIPf/4h6GDEjA/aNPnY5jTtLpuSksfO0nNM3x0bJ5FbFuawdGCvuXNL321AdbcLvk2M03JnzlpsXR3NrGovW2KEkksUJveqVi32EWra8mOyWOGJcNqQx36Qke4mLdPPV+OarqdBwTJFboTa88+9FW3C4h1+6EjQgCDEqLp6S6jo/L9jodxwSJFXpz0vY3NPNyUQXTJuThibEfpUiRmeQhK9nLUx/Y3IORwj6d5qT9ffl2jrS0cc9FI5yOYoLIJcI3zxvGh5v3ULKzzuk4Jgis0JuT0tjSxvPLtnHJqVmcmpPsdBwTZLedPZQEj5tnPix3OooJAiv05qTMXVXJnkPN1pqPUKkJscw4awjz1+6k6sARp+OYXrJx9KbHWtp8jP76dN5wCWN/tcrpOKaP3H3hcK6aOYPm+V7YUOR0HNML1qI3PTZvVRVNLW3kp8cjNktlxMpLiycrycvu+iaqD1qrPpxZoTc90tLm4/dLN5PojSEtweacj3SD0uMB+MO7NgInnAVU6EVkioiUikiZiDzYxf6LRGSViLSKyI2d9t0pIpv9X3cGK7hxxqsrK6ncf4T89ASsLR/54mJcZCV7mV20w/rqw1i3hV5E3MAsYCowGrhVREZ3OmwH8E3gxU7nZgA/Bc4GJgM/FZH03sc2TmhqbePJpWVMHJxGWkKs03FMP8lLi0cQnlxa5nQUc5ICadFPBspUtVxVm4HZwPSOB6jqNlVdB/g6nXsV8Laq7lPV/cDbwJQg5DYOmFNcSdWBI9x/xShrzUcRb4yLGZMH80pxBRX7Djsdx5yEQAp9HtBx3tJK/7ZABHSuiNwjIsUiUlxbWxvgS5v+1NjSxqylZRQOTefCgkyn45h+9t1LRuJyCf+9dLPTUcxJCImLsar6tKoWqmphVlaW03FMF2av2MGuusb21ryNtIk6OalxfOPsIcxdVcXWPQ1OxzE9FEihrwIGd3ie798WiN6ca0LEwcMtjL3tehbN+wnnnjLA6TjGIfdecgovvfggzRde5HQU00OBFPoioEBEhouIB5gBzA/w9ZcAV4pIuv8i7JX+bSaM/PfSzbS2+Rg6IMFa81EsOzmOvLR49jc0s2yLzWwZTrot9KraCsykvUBvAuao6kYReUxEpgGIyFkiUgncBDwlIhv95+4Dfkb7L4si4DH/NhMmtu5p4Pll28hKjiPRYzdSR7vc1Dg8MW5+vrCENp/NVx8uAvrkquoiYFGnbY92eFxEe7dMV+c+BzzXi4zGQb9ctAmP28XgjHino5gQ4BJhSEYCG3fWMXdlJTefNbj7k4zjQuJirAlNn2zZw9slNXz30pF4bP1Q4zcgycMZQ9J44q1SDjW1Oh3HBMA+vaZLbT7lZws2kZcWz90XDHc6jgkhAvzk2tHU1jfxx/dsaoRwYIXedOmlFTvYVF3Hg1NPIy7W7XQcE2ImDUnn+omDeObDcrbZcMuQZ1fXzJfsOtjIqTOuY5E3htN/tdLpOCZEPT7rPr5RcYCHhz7NC98620ZkhTBr0ZsvUFV+8voGfAojMhPtw2uOy+N2MSQjgU+27OWVlZVOxzEnYIXefMGbG3bxdkkNg9PjrcvGdCs7JY7JwzL4xcJN7K5vdDqOOQ4r9OaYg4dbeHT+RsYMSiE31YZTmu4J8KsbxnGkuY3/eKPE6TjmOKzQm2N+tXgT+xqa+c0N47EeGxOoU7KS+P5lI1m4rpq3S2qcjmO6YIXeAPD+57XMLqrgWxcOZ2xeqtNxTJi556JTOC0nmUf+sZ59Dc1OxzGd2Kgbw+76Rh6Ys4bXX32EcctSYOr7TkcyYcYT42Luyw+zYWcdP8p7lmfuKLQL+SHEWvRRzudTHpizlvrGVgqyk3DZh9OcpERvDEMyEnhn026e/2Sb03FMB1boo9wzH5bz4eY9PHrdaBI8NsrG9E5OahxfOS2bXy76jJKddU7HMX5W6KPYmooDPLGklKljc/j65CFOxzERQIAnbhxPWkIsM19axeFmmwsnFFihj1L7G5r5/kurGZgSx6+/Nt76U03QDEjy8rtbJrJ1TwOPzNuAqk1n7DQr9FGopc3HvS+s5IlZ9/HmPx4lNSHW6Ugmwpw3MpP7LivgtdVVPP1BudNxop6Nuokyqsqjr29kefk+RmQlkhxnPwKmb3z/KwVsrjnEr9/8jFOykrh89ECnI0WtgFr0IjJFREpFpExEHuxiv1dEXvbv/1REhvm3DxORIyKyxv/1xyDnNz30l0+28dKKHdx7ySlkJXmdjmMimMsl/J+bJjB2UCr3zV7NZ7vs4qxTui30IuIGZgFTgdHArSIyutNhdwP7VXUk8J/Abzrs26KqE/1f3wlSbnMS3v+8lp8tKOHK0QP5tytPdTqOiQLxHjfP3FFIUlwMd/+lmD2HmpyOFJUCadFPBspUtVxVm4HZwPROx0wHnvc/fhW4TOzqXkhZuX0/9/59JafmpPCft0zE5bJ/HtM/clLj+NMdZ7G3oYk7nl3BwcMtTkeKOoEU+jygosPzSv+2Lo/xLyZ+EBjg3zdcRFaLyPsicmEv85qTsL7yIN98bgUDU+J4/l/OItFr/fKmf43LT+Wp2wsp232IO/+8wpYg7Gd9PeqmGhiiqpOA+4EXRSSl80Eico+IFItIcW1tbR9Hii6lu+q5/blPSYmP5YVvnU12SpzTkUyUunhUFk9+fRLrqw5y11+KONLc5nSkqBFIoa8COi71nu/f1uUxIhIDpAJ7VbVJVfcCqOpKYAswqvMbqOrTqlqoqoVZWVk9/y5Ml7bUHuIbf/oUb4yLl/7XOQxKs6mHjbOuHJPD726ZSPG2fdzzt2IaW6zY94dACn0RUCAiw0XEA8wA5nc6Zj5wp//xjcBSVVURyfJfzEVERgAFgA2q7QdrKw5w8x+XAcoL3zqHIQMSnI5kDADXTRjEb24Yz4eb93DHcys4eMT67Ptat4Xe3+c+E1gCbALmqOpGEXlMRKb5D3sWGCAiZbR30RwdgnkRsE5E1tB+kfY7qrovyN+D6eS90t3MeHo58R43c759LiOzk5yOZMwX3FQ4mN/fOonVO/Zz8x+XUX3wiNORIlpAV+VUdRGwqNO2Rzs8bgRu6uK8ucDcXmY0PTB3ZSX/Pncdp+Yk8+d/OYvsZOuTN6Fp2oRBDEj08O2/reSGP3zC83dNpmBgstOxIpJNgRAh2nzK/32rlAdeWcvZIzKYfc85VuRNyDt/ZCYvf/scWnzKDf/zCe+W7nY6UkSyQh8B9h5q4s7nVvDfS8u4uTCfP39zMslxNn+NCQ9jBqXy2r3nkZeewF1/KeK3b5XS5rOJ0ILJCn2YW7l9P9f+90cUbdvH4zeM5/EbJ+CJsX9WE14GZyQw77vnceMZ+fx+aRnf/PMKW5IwiKwihKnmVh+/e+dzbnlqGbFuF3PvPY+bzxrc/YnGhKi4WDdP3DSB39wwjk+37mPqf33APzfZYuPBYIU+DG2oOsi0Jz/id+9s5upxubwx8wJb0NtEjFvOGsJr955HWryHu58v5v97eQ0HDlvrvjfsXvgwcri5lSeXlvHUB+UMSPTwzB2FXGFTv5oINDYvlTf+9QKefLeMP7xbxoeb9/C/p43mmnG5tkjOSbBCHwZ8PmXuqkqeWFLK7vombjgjn0evHW0LhpiI5olxcf8Vo7hqzEB+9Oo6Zr64mr8M3cYj145m4uA0p+OFFSv0IUxV+bhsL79avImNO+uYODiN/7ntDM4cmuF0NGP6zZhBqcyfeQGvFFfwf976nOtnfcz0iYN44IpT7Y7vAFmhD0E+n/LPz3Yz690y1lQcIC8tnt/fOonrxtufrSY6uV3CjMlDuHbCIP743hae+bCcBeuqmTZhEPdecgqj7EarE7JCH0IaW9pYsK6aZz4op7Smnvz0eH5+/VhuPDOfuFi30/GMcVySN4YfXnUqt587lGc+KOeFT3cwb3UVV44eyL+cP5xzRmRYY6gLVuhDQNnuel74dAdzV1ZS19hKQXYSv715AtMmDCLGbQOjjOlsYEocj1w7mu9eOpK/fLyV55dt562SGkZkJfL1yUO48cx80hI8TscMGVboHVJ98AgL11XzxtqdrK08SKxbmDI2l69PHmKtEmMClJHo4f4rT+XeS0aycH01L3y6nZ8v3MTjb5ZyyalZXDthEJefnk2CJ7pLXXR/9/1IVSmtqee90lreKamhePt+AMbmpfDw1afxtTPyybTFuo05KfEeNzeemc+NZ+ZTsrOOV1ZWsHBdNW+V1BAf6+bS07K49NRsLj41KyrngLJC34d2HjjCiq37WF6+l/c/r6X6YCMAp+em8MMrR3HN+EEMz0x0OKUxkWX0oBR+OmgMj1wzmqJt+1iwbidvbaxh0fpdQHvj6sKCLM4ensGZQ9OjYl4oK/RBcqS5jZLqg6yrbP8q2raPyv3tc2wne2M4b+QAfnB5ARePyiYnNfpaFMb0N7dLOGfEAM4ZMYCfTR9LSXUd75XW8u5nu3nmg3L+570tuKR9+OYZQ9IYl5/GhPxURmQl4XZFVtepFfoeamxpY8e+w5TXHuLzmkOU1tTz+a56yvc0HJtxLzvZy6Qhadx1/nAmD8/g9NyUiPvBMSaciAhjBqUyZlAq37t0JA1NrazecYAVW/fy6dZ9vLKykueXbQcgweNm1MBkTh2YzKicZEYNTGLYgEQGpcWH7efYCn0nDU2t1NQ1UlPXRNWBI1TtP0LVgcNU7j/C9r2H2XnwCOqfQVUEhmQkMGpgMlPG5jA+P43x+akMtAW4jQlpid4YLijI5IKCTKB9PYetew6xtuIg66sO8nlNPf/8rIaXiyuOneNxuxgyIIGhGQnkpceTlxZPfnoCuWlxDEyJIyvJG7IzxwZU6EVkCvBfgBv4k6r+utN+L/BX4ExgL3CLqm7z73sIuBtoA76vqkuClv4EWtt8NDS3Ud/YQn1jK3VHWqhrbOXA4WYOHmnhwOEW9h1uZu+hJvYeamZvQzO19U0camr90mtlJXvJS4vnrGHpDMvMZ3hmIsMzExmZnRT1V/ONiQRulzAyO5mR2cnccGb+se17DjWxueYQ2/Y2sG1PA1v3NLBj32FWbNtHfeOXa0VGooesJC8DkjwMSPIyINFDWkIs6Qnt/02JjyUlLpaUuBiS42JJjoshwePu81F23VYp/+Les4ArgEqgSETmq2pJh8PuBvar6kgRmQH8BrhFREbTvpj4GGAQ8I6IjFLVoC/9vvdQE1/9wyc0NLXS0NxKY4vvhMe7XUJ6QiwDEtv/UcYMSiE7OY7sFC8DU7wMTI4jNy2e3NQ4u1nJmCiVmeQlM8nLuacM+NK+usYWqvYfYVddI7v9vQC76hqPNR43VB1kz6GmLn8hHOV2CWW/mNqX3wIQWIt+MlCmquUAIjIbmA50LPTTgf/tf/wq8KS0/4qaDsxW1SZgq3/x8MnAsuDE/3/iPW4mDUlj2Za9pCd4cIvgcgkxLsHd8b9u17HHR7X5lNr6Jmrrm9i4M9jJQtejO+sAeOypZV96fqJ9PX1ur+XcazmZM5q5XUJ2spfsZC9Ke41pbfPR6lNafUqbT2nz+fD5YMbTy4+d9/K3z+2TPKJ64iW7RORGYIqqfsv//HbgbFWd2eGYDf5jKv3PtwBn0178l6vq3/3bnwUWq+qrnd7jHuAegCFDhpy5ffv2k/6GbrEfMmNMmOpNoReRlapa2NW+kOhgVtWngacBCgsLe7VYZF/9RjTGmHAVyCXiKqDjGnX5/m1dHiMiMUAq7RdlAznXGGNMHwqk0BcBBSIyXEQ8tF9cnd/pmPnAnf7HNwJLtb1PaD4wQ0S8IjIcKABWBCe6McaYQHTbdaOqrSIyE1hC+/DK51R1o4g8BhSr6nzgWeBv/out+2j/ZYD/uDm0X7htBb7XFyNujDHGHF+3F2P7W2FhoRYXFzsdwxhjwsqJLsaG5m1cxhhjgsYKvTHGRDgr9MYYE+Gs0BtjTIQLuYuxIlILnPytsZAJ7AlSnGCyXD1juXrGcvVMJOYaqqpZXe0IuULfWyJSfLwrz06yXD1juXrGcvVMtOWyrhtjjIlwVuiNMSbCRWKhf9rpAMdhuXrGcvWM5eqZqMoVcX30xhhjvigSW/TGGGM6sEJvjDERLmILvYg8ICIqIplOZzlKRH4mIutEZI2IvCUig0Ig0xMi8pk/1zwRSXM601EicpOIbBQRn4g4OhRORKaISKmIlInIg05m6UhEnhOR3f5V3kKGiAwWkXdFpMT/b3if05kARCRORFaIyFp/rv9wOtNRIuIWkdUisiDYrx2RhV5EBgNXAjucztLJE6o6XlUnAguARx3OA/A2MFZVxwOfAw85nKejDcDXgA+cDCEibmAWMBUYDdzqX/g+FPwFmOJ0iC60Ag+o6mjgHOB7IfL/rAn4iqpOACYCU0TkHGcjHXMfsKkvXjgiCz3wn8CPgJC60qyqdR2eJhIC+VT1LVU9ukz9ctpXAQsJqrpJVUudzkH7gvZlqlquqs3AbNoXvnecqn5A+xoQIUVVq1V1lf9xPe0FLM/ZVKDtDvmfxvq/HP8cikg+cA3wp754/Ygr9CIyHahS1bVOZ+mKiPxCRCqAbxAaLfqO7gIWOx0iBOUBFR2eVxICRStciMgwYBLwqcNRgGNdJGuA3cDbqhoKuX5He+PU1xcvHhKLg/eUiLwD5HSx68fAw7R32zjiRNlU9XVV/THwYxF5CJgJ/NTpTP5jfkz7n9sv9HWenmYz4UtEkoC5wA86/UXrGP8qdxP916PmichYVXXsGoeIXAvsVtWVInJJX7xHWBZ6Vb28q+0iMg4YDqwVEWjvhlglIpNVdZeT2brwArCIfij03WUSkW8C1wKXaT/fWNGD/19OskXuT4KIxNJe5F9Q1decztOZqh4QkXdpv8bh5MXs84FpInI1EAekiMjfVfW2YL1BRHXdqOp6Vc1W1WGqOoz2P7HP6K8i3x0RKejwdDrwmVNZjhKRKbT/yThNVQ87nSdEFQEFIjJcRDy0r4k83+FMIU3aW1rPAptU9bdO5zlKRLKOjiwTkXjgChz+HKrqQ6qa769ZM4ClwSzyEGGFPgz8WkQ2iMg62ruXQmHI2ZNAMvC2f9jnH50OdJSIfFVEKoFzgYUissSJHP6L1TOBJbRfVJyjqhudyNKZiLwELANOFZFKEbnb6Ux+5wO3A1/x/1yt8bdYnZYLvOv/DBbR3kcf9OGMocamQDDGmAhnLXpjjIlwVuiNMSbCWaE3xpgIZ4XeGGMinBV6Y4yJcFbojTEmwlmhN8aYCPf/A/PwL4ZS8WUUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t_p(-2,2)  #t:[-2,2], df=10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "#基于原始数据的t分布均值和置信区间\n",
    "def t_interval(x,b=0.95):  #这里b为置信水平，通常取95%\n",
    "    a=1-b \n",
    "    n = len(x) \n",
    "    ta=st.t.ppf(1-a/2,n-1);ta     \n",
    "    from math import sqrt \n",
    "    se=x.std()/sqrt(n)\n",
    "    return(x.mean()-ta*se, x.mean()+se*ta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(166.28691128155606, 170.7515502569055)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_interval(BSdata['身高']) #身高均值的 95%的置信区间"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 　6.3.2 参数的假设检验"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6.3.2.2 样本均值 t 检验"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "样本均值： 168.51923076923077\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Ttest_1sampResult(statistic=2.2656106477907243, pvalue=0.02775093534857837)"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#单样本 t 检验函数进行均值的 t 检验 \n",
    "print(\"样本均值：\",BSdata.身高.mean())\n",
    "st.ttest_1samp(BSdata.身高,popmean = 166)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_1sampResult(statistic=-1.3316948082433964, pvalue=0.188881956923451)"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "st.ttest_1samp(BSdata.身高,popmean = 170)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 　6.3.3 统计推断的可视化"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6.3.3.1 均值推断的可视化函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "#定义单样本均值t检验图\n",
    "def ttest_1plot(X,mu=0,k=0.1): \n",
    "    df=len(X)-1  #df=n-1\n",
    "    t1p=st.ttest_1samp(X, popmean = mu);\n",
    "    x=np.arange(-4,4,k); y=st.t.pdf(x,df)\n",
    "    t=abs(t1p[0]);p=t1p[1]\n",
    "    x1=x[x<=-t]; y1=y[x<=-t];\n",
    "    x2=x[x>=t]; y2=y[x>=t];\n",
    "    print(\"  样本均值： \\t%8.4f \"%X.mean())\n",
    "    print(\"  单样本t检验:    t=%6.3f  p=%6.4f\"%(t,p))\n",
    "    t_interval=st.t.interval(0.95,len(X)-1,X.mean(),X.std())\n",
    "    print(\"   t置信区间:\\t(%7.4f, %7.4f)\"%(t_interval[0],t_interval[1]))\n",
    "    plt.plot(x,y); plt.hlines(0,-4,4);\n",
    "    plt.vlines(x1,0,y1,colors='r'); plt.vlines(x2,0,y2,colors='r');\n",
    "    plt.vlines(st.t.ppf(0.05/2,df),0,0.2,colors='b');\n",
    "    plt.vlines(-st.t.ppf(0.05/2,df),0,0.2,colors='b');\n",
    "    plt.text(-0.6,0.2,r\"$\\alpha$=%3.2f\"%0.05,fontsize=15);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  样本均值： \t168.5192 \n",
      "  单样本t检验:    t= 2.266  p=0.0278\n",
      "   t置信区间:\t(152.4217, 184.6167)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ttest_1plot(BSdata.身高,166)  #总体均值为166时的推断图 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  样本均值： \t168.5192 \n",
      "  单样本t检验:    t= 1.332  p=0.1889\n",
      "   t置信区间:\t(152.4217, 184.6167)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ttest_1plot(BSdata.身高,170)  #总体均值为170时的推断图 "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
